Cohen-Macaulayness of associated graded rings of Gorenstein monomial curves
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929403028570112 |
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| author | Katsabekis, Anargyros |
| author_facet | Katsabekis, Anargyros |
| contents | Let $C$ be a Gorenstein noncomplete intersection monomial curve in the 4-dimensional affine space with defining ideal $I(C)$. In this article, we use the minimal generating set of $I(C)$ to give a criterion for determining whether the tangent cone of $C$ is Cohen-Macaulay. We also show that if the tangent cone of $C$ is Cohen-Macaulay, then the minimal number of generators of the ideal $I(C)_{\ast}$ is either $5$ or an even integer of the form $2d+2$, for a suitable integer $d$. Additionally, we provide a family of Gorenstein noncomplete intersection monomial curves $C$ whose tangent cone is Cohen-Macaulay and the minimal number of generators of $I(C)_{\ast}$ is large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01983 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cohen-Macaulayness of associated graded rings of Gorenstein monomial curves Katsabekis, Anargyros Commutative Algebra 13H10, 13A30, 13P10, 14H20 Let $C$ be a Gorenstein noncomplete intersection monomial curve in the 4-dimensional affine space with defining ideal $I(C)$. In this article, we use the minimal generating set of $I(C)$ to give a criterion for determining whether the tangent cone of $C$ is Cohen-Macaulay. We also show that if the tangent cone of $C$ is Cohen-Macaulay, then the minimal number of generators of the ideal $I(C)_{\ast}$ is either $5$ or an even integer of the form $2d+2$, for a suitable integer $d$. Additionally, we provide a family of Gorenstein noncomplete intersection monomial curves $C$ whose tangent cone is Cohen-Macaulay and the minimal number of generators of $I(C)_{\ast}$ is large. |
| title | Cohen-Macaulayness of associated graded rings of Gorenstein monomial curves |
| topic | Commutative Algebra 13H10, 13A30, 13P10, 14H20 |
| url | https://arxiv.org/abs/2311.01983 |